Question

1. Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread. Hint: make sure you interpret these measures in the context of the data and pay attention to the unit of measurement in Excel.

2. Date	Weekly Return BIT
   11/3/13	-46.16
   18/3/13	-0.01
   25/3/13	39.23
   1/4/13	13.07
   8/4/13	23.93
   15/4/13	41.36
   22/4/13	26.5
   29/4/13	20.39
   6/5/13	25.5
   13/5/13	42.52
   20/5/13	37.88001
   27/5/13	15.66
   3/6/13	20.98
   10/6/13	25.28
   17/6/13	11.97
   24/6/13	-2.46
   1/7/13	14.95
   8/7/13	-3.5
   15/7/13	-8
   22/7/13	-0.05
   29/7/13	25.49
   5/8/13	4.099998
   12/8/13	9.529999
   19/8/13	58.75
   26/8/13	36.12
   2/9/13	47.87
   9/9/13	43.09
   16/9/13	42.08
   23/9/13	40.24001
   30/9/13	51.77
   7/10/13	93.52
   14/10/13	113.89
   21/10/13	133.5
   28/10/13	231.05
   4/11/13	447.08
   11/11/13	874.55
   18/11/13	1091.99
   25/11/13	916.27
   2/12/13	927.8199
   9/12/13	681.78
   16/12/13	789.11
   23/12/13	899
   30/12/13	937.92
   6/1/14	877.1
   13/1/14	900
   20/1/14	828.99
   27/1/14	750
   3/2/14	640
   10/2/14	628.37
   17/2/14	550
   24/2/14	574.73
   3/3/14	569.53
   10/3/14	546.83
   17/3/14	460
   24/3/14	418.31
   31/3/14	375
   7/4/14	467.54
   14/4/14	369
   21/4/14	402.16
   28/4/14	356
   5/5/14	410.9
   12/5/14	548.66
   19/5/14	652.71
   26/5/14	650
   2/6/14	571.71
   9/6/14	590
   16/6/14	565
   23/6/14	561.2
   30/6/14	592.14
   7/7/14	514.12
   14/7/14	500.84
   21/7/14	565.93
   28/7/14	587.76
   4/8/14	484.97
   11/8/14	443
   18/8/14	410.53
   25/8/14	437.92
   1/9/14	462.43
   8/9/14	324.44
   15/9/14	360.15
   22/9/14	253.36
   29/9/14	381.64
   6/10/14	385.55
   13/10/14	349.98
   20/10/14	319.9
   27/10/14	340.98
   3/11/14	363.96
   10/11/14	348.09
   17/11/14	371.5
   24/11/14	376
   1/12/14	319.55
   8/12/14	334.97
   15/12/14	343.46
   22/12/14	262.8
   29/12/14	250.09
   5/1/15	190.02
   12/1/15	380.51
   19/1/15	189.48
   26/1/15	209.59
   2/2/15	223.9
   9/2/15	223.5
   16/2/15	254.85
   23/2/15	251.34
   2/3/15	305.86
   9/3/15	249.82
   16/3/15	280
   23/3/15	220.56
   30/3/15	279.94
   6/4/15	265
   13/4/15	200
   20/4/15	224.68
   27/4/15	195.91
   4/5/15	245.03
   11/5/15	227.36
   18/5/15	269.69
   25/5/15	228.8
   1/6/15	220.5
   8/6/15	212.87
   15/6/15	225.62
   22/6/15	262.18
   29/6/15	343.58
   6/7/15	312.15
   13/7/15	301.96
   20/7/15	315
   27/7/15	262.04
   3/8/15	229.08
   10/8/15	257.53
   17/8/15	220.4
   24/8/15	249.46
   31/8/15	230.8
   7/9/15	223.27
   14/9/15	246.48
   21/9/15	250.66
   28/9/15	239.59
   5/10/15	273.53
   12/10/15	300.01
   19/10/15	377.69
   26/10/15	451.39
   2/11/15	371.79
   9/11/15	376.89
   16/11/15	418.39
   23/11/15	440.58
   30/11/15	505.46
   7/12/15	516.24
   14/12/15	481.21
   21/12/15	482.38
   28/12/15	542.2
   4/1/16	454.28
   11/1/16	473.92
   18/1/16	432.58
   25/1/16	429.39
   1/2/16	467.05
   8/2/16	509.61
   15/2/16	506.68
   22/2/16	448.07
   29/2/16	443.69
   7/3/16	484.58
   14/3/16	489.97
   21/3/16	485.82
   28/3/16	455.66
   4/4/16	474.93
   11/4/16	516.19
   18/4/16	488.28
   25/4/16	555.87
   2/5/16	542.67
   9/5/16	512.75
   16/5/16	601.27
   23/5/16	688.69
   30/5/16	803.09
   6/6/16	953.05
   13/6/16	805.65
   20/6/16	797.08
   27/6/16	771.54
   4/7/16	795.01
   11/7/16	793.52
   18/7/16	723.18
   25/7/16	687.93
   1/8/16	650.5
   8/8/16	660
   15/8/16	670
   22/8/16	715.6
   29/8/16	714
   5/9/16	734.99
   12/9/16	686.2
   19/9/16	719.42
   26/9/16	715.57
   3/10/16	754
   10/10/16	761.02
   17/10/16	825
   24/10/16	825.83
   31/10/16	831.9
   7/11/16	900.52
   14/11/16	902.97
   21/11/16	924.27
   28/11/16	975.2
   5/12/16	1006.2
   12/12/16	1135.94
   19/12/16	1281.4
   26/12/16	1144.41
   2/1/17	995.16
   9/1/17	1123.2
   16/1/17	1138.34
   23/1/17	1247.74
   30/1/17	1241.48
   6/2/17	1275.95
   13/2/17	1453.46
   20/2/17	1590.27
   27/2/17	1549.1
   6/3/17	1262.27
   13/3/17	1177.61
   20/3/17	1372.88
   27/3/17	1512.83
   3/4/17	1488.75
   10/4/17	1583.46
   17/4/17	1681.71
   24/4/17	2096.67
   1/5/17	2495.07
   8/5/17	2760.85
   15/5/17	2994.79
   22/5/17	3393.27
   29/5/17	3789.46
   5/6/17	3488.86
   12/6/17	3403.31
   19/6/17	3242.76
   26/6/17	3315.51
   3/7/17	2410
   10/7/17	3441.5
   17/7/17	3429.74
   24/7/17	3960.53
   31/7/17	5218.14
   7/8/17	5198.76
   14/8/17	5520
   21/8/17	5918.4
   28/8/17	5219.46
   4/9/17	4493.05
   11/9/17	4525.38
   18/9/17	5465.36
   25/9/17	5787.35
   2/10/17	7126.76
   9/10/17	7613.93
   16/10/17	7918.65
   23/10/17	9592.39
   30/10/17	7824.89
   6/11/17	10593.55
   13/11/17	12197.99
   20/11/17	14924.19
   27/11/17	21084.87
   4/12/17	25886.55
   11/12/17	18839.79
   18/12/17	18950.74
   25/12/17	22762.21
   1/1/18	18941.51
   8/1/18	15048.37
   15/1/18	14345.12
   22/1/18	10125.82
   29/1/18	10282.72
   5/2/18	13238.45
   12/2/18	12200.72
   19/2/18	14663.94
   26/2/18	12043.73
   5/3/18	10546.88
   12/3/18	10939.19
   19/3/18	8735.98
   26/3/18	9030.39
   2/4/18	10554.32
   9/4/18	11257.21
   16/4/18	12332.76
   23/4/18	12582.62
   30/4/18	11460.03
   7/5/18	11218.46
   14/5/18	9652.02
   21/5/18	10133.1
   28/5/18	8856.31
   4/6/18	8617.19
   11/6/18	8152.91
   18/6/18	8389.05
   25/6/18	8853.63
   2/7/18	8455.52
   9/7/18	9847.28
   16/7/18	11014.06
   23/7/18	9459.81
   30/7/18	8619.77
   6/8/18	8820.44
   13/8/18	9072.49
   20/8/18	9981.22
   27/8/18	8702.43
   3/9/18	8958.83
   10/9/18	9018.22
   17/9/18	9039.68
   24/9/18	9164.69
   1/10/18	8635.74
   8/10/18	8905.48
   15/10/18	8919.61
   22/10/18	8808.97
   29/10/18	8741.39
   5/11/18	7479.24
   12/11/18	5335.57
   19/11/18	5486.65
   26/11/18	4814.89
   3/12/18	4340.44
   10/12/18	5496.18
   17/12/18	5356.26
   24/12/18	5586.6
   31/12/18	4808.14
   7/1/19	4862.34
   14/1/19	4842.09
   21/1/19	4634.24
   28/1/19	5032.33
   4/2/19	4983.2
   11/2/19	5113.99
   18/2/19	5240.09
   25/2/19	5455.14
   4/3/19	5526.45
   11/3/19	5517.53
   18/3/19	5638.09
   25/3/19	7153.71
   1/4/19	7114.66
   8/4/19	7337.26
   15/4/19	7305.25
   22/4/19	8020.41
   29/4/19	9862.31
   6/5/19	11784.94
   13/5/19	12517.35
   20/5/19	12506.94
   27/5/19	10883.83
   3/6/19	12861.26
   10/6/19	15472.87
   17/6/19	15080.16
   24/6/19	16268.05
   1/7/19	14557.08
   8/7/19	14957.73
   15/7/19	13791.59
   22/7/19	16032.89
   29/7/19	16937.56
   5/8/19	15248.79
   12/8/19

Answer 1

I am assuming the unit of return is %.

The following output is obtained using the 'Descriptive Statistics' tools in Excel.

Steps:

1. Input the data in Excel.
2. click the data whose summary has to be obtained. In our case 'Weekly Return'
3. Click on 'Data' on the toolbar and then select 'Data Analysis' on the top right corner
4. Select 'Descriptive Statistics' from the options.
5. Fill the required information and the output will be obtained.

Weekly Return
Mean	3556.180
Standard Error	269.817
Median	734.990
Mode	#N/A
Standard Deviation	4938.460
Sample Variance	24388386.970
Kurtosis	2.270
Skewness	1.638
Range	25932.710
Minimum	-46.160
Maximum	25886.550
Sum	1191320.170
Count	335.000

The yellow coloured values are the measures of location and the green coloured are the measures of spread. With the help of both of these measures we can interpret the shape of the data.

Measures of location:

Mean tells us on an average what weekly return would be. It is 3556.180%. It is too far from the -46.16% in 2013 and from the 25886.6% in 2019.

This can be greatly affected by the extreme values.

Median is point where below it 50% (half) of the data lies and 50% lies above it. If median is 734.99%, that means 50% of the returns calculated over the 6 years period were below this point and rest above it.

Like mean it is not affected by the extreme values.

Mode is the poit with the highest frequency It is difficult to determine in this data since the returns haven't repeated to calculate the highest frequecny.

Measures of spread: It tells us how much spread, variation is there in the data.

Range is the diffeence between the maximum and the minimum value. It is 25932.710. This is very high but it only measures the absolute difference and ignores the intermediate values.

Standard deviation (square root of variance) is the average deviation of the values from the mean. Each value would deviate from the mean on some level. SD calculates the average deviation. the higher the value the higher would be the variation between the values. It is 4938.460%. On average the values differ by 4938.46% from the mean return.

Interquartile range which is the difference between the 1st and 3rd quartile tells us about the central 50% of the data. it is 5169.73%.

Shape:

It can be determined by the skewness. It is 1.638. This means the data is positively skewed. This means the data has the few high scores shifting towards the mean. It can also be interpreted by looking at the mean and median. Mean > median.

Kurtosis tells us about the shape of the distribution, its tails. High kurtosis have fatter tails means they contain high extreme values and more like a normal distribution. It is 2.27 which is high and closer to kurtosis of normal distribution (3).