Question

The following data represent the ages in years of a sample of 25 employees from a government department:

            31        43        56        23        49        42        33        61        44        28

            48        38        44        35        40        64        52        42        47        39

            53        27        36        35        20

1. Construct a stem and leaf display for the ages.

2. Find the median age.

           

3. Find the lower quartile of the ages.

           

4. Find the upper quartile of the ages.

           

5. Find the 60th percentile of the ages.

           

6. Compute the range and interquartile range of the data.

7. Compute the sample mean age.

           

8. Compute the sample variance, and sample standard deviation.

           

1. Calculate the 4^th decile of the data.            

            

10. Compute the 8^th decile of the data.                

11. Calculate the 1^st quintile

l. Calculate the 2^nd quintile

m. Construct a relative frequency distribution for the data, using five class intervals and the value 20 as the lower limit of the first class.

           

14. Construct a relative frequency histogram for the data, using the relative frequency distribution constructed in Question m.

           

Answer 1

(i) Stem & Leaf

STEM	LEAF
2	0378
3	1355689
4	022344789
5	236
6	14

Procedure:

Stem and Leaf display process is as same as the Tally mark frequency method. But in the tally mark frequency method we use the storkes and count those strokes to make frequency. In Stem and Leaf we observe the given value and write those Tenth Place as STEM i.e if the the value in the given series is 10 we write its stem as 1, if the value in the given series is 20, 23, 29 then we write its stem value as 2, if the given values in 30s then we write its stem value as 3......... if the given values in 90s then we write its stem value as 9.

If we observe in the given series we have the values relatd to 20s, 30s, 40s, 50s and 60s, So We took the stem values as 2, 3, 4,5 and 6.

Coming to the Leaf value. If the value is 20 then write the UNIT value (i.e 0) in LEAF, if the Value is 64 write the unit value i.e 4 in LEAF, If the value is 53 the STEM IS 5 and LEAF IS 3, If the value is 31 then the STEM IS 3 and 1 IS LEAF.......

	X
	20
	23
	27
	28
	31
	33
	35
	35
	36
	38
	39
	40
	42
	42
	43
	44
	44
	47
	48
	49
	52
	53
	56
	61
	64
MEDAIN	42
Q1	34
Q3	48.5
P60	43.6
R	44
IQR	14.5
MEAN	41.2
VARIANCE	119.8400
S.D	10.9471

The above calculatins are made using EXCEL.

Procedure:

Step1: Type all the given values in Excel Sheet

Step2: Make the given data in Ascending Order. For this Select the Data and Select the SORT & FILTER option from MENU and that select A to Z; this will makes the given data in ASCENDING ORDER

Step3: Put the cursor in Cell A27 because the given values are 25 and heading x occupied upto A26 so we want to put the cursor at A27(or at your required place)

Step4: Select the FORMULAS from menu; from that select INSERT FUNCTIONS which is with the logo fx. After selectin INSERT FUNCTION we will get a List of Formulae Window.

Step5: From that window Select MEDIAN; after selecting MEDIAN a window will open in that fill the value as A2;A26 and Press OK, it will gives the MEDIAN value.

Similarly do the same procedure;

For Quartiles: Select QUARTILE.EXC in this for first quartile give 1 and for 3rd quartile give the Quar as 3

For Percentile: Select PERCENTILE.EXC in this for the 60 the percentile give the K value as 0.6 i.e 60/100

For Mean, Variance and S.D : Select AVERAGE, VAR.P and STDEV.P

Note: For all the Measures we have to fill the Array with the cell values A2:A26