Question

1. 25 children were sampled having the following ages.

5.0, 5.2, 5.2, 4.6, 5.9

6.5, 6.2, 4.5, 3.9, 4.9

5.2, 5.1, 4.9, 6.2, 6.5

6.3, 4.9, 2.1, 3.4, 3.9

4.2, 5.3, 6.1, 1.5, 1.7

Prepare a frequency and relative frequency table.  Plot the histogram using 11 intervals.

2. Find out the average , median and mode (if any) of the following sample:

35, 82, 83, 90, 77, 84,92,77,83, 81

3. What is the value of variance and standard deviation in problem 2?

Answer 1

1) Frequency and relative frequency table:

Freq	Rel.freq
5	0.041946
5.2	0.043624
5.2	0.043624
4.6	0.038591
5.9	0.049497
6.5	0.05453
6.2	0.052013
4.5	0.037752
3.9	0.032718
4.9	0.041107
5.2	0.043624
5.1	0.042785
4.9	0.041107
6.2	0.052013
6.5	0.05453
6.3	0.052852
4.9	0.041107
2.1	0.017617
3.4	0.028523
3.9	0.032718
4.2	0.035235
5.3	0.044463
6.1	0.051174
1.5	0.012584
1.7	0.014262

11 interval data set:

1-1.5	1
1.6-2	1
2.1-2.5	1
2.6-3	0
3.1-3.5	1
3.6-4	2
4.1-4.5	2
4.6-5	5
5.1-5.5	5
5.6-6	1
6.1-6.5	6

Histogram for 11 interval data set

2)

average=78.4

median=82.5

mode=83

3)

variance=255.6

standard deviation=15.9874

using MS-excel we find descriptive statistic:

Mean	78.4
Standard Error	5.05568986
Median	82.5
Mode	83
Standard Deviation	15.9874951
Sample Variance	255.6
Kurtosis	7.69471681
Skewness	-2.6252749
Range	57
Minimum	35
Maximum	92
Sum	784
Count	10
Largest(1)	92
Smallest(1)	35
Confidence Level(95.0%)	11.436765