Question

Question one

The following table gives the distribution of marks of 60 students in applied statistics test

Marks	0 - 9	10 - 14	15 - 19	20 - 24	25 - 34
Frequency	13	19	12	7	9

1. Calculate the:
2. Mean, mode, median and define statistics                     
3. Lower quartile , upper quarter, Interquartile range
4. A researcher has extracted two samples from the same target population, sample A and sample B. Sample A has a mean of 25 kg while sample B has a mean twice that of sample A. Sample size of sample A is three times more than that of sample B. Sum of sample sizes is 60. Calculate:

1. Mean of sample B (1mark)
2. Sample size of sample A and sample B
3. Summation of x variables for sample A and sample B
4. Standard deviation of sample A and sample B, consider ungrouped data

Answer 1

b)

Marks	Frequency (f)	Mid Point (m)	f*m
0 - 9	13	4.5	58.5
10-14'	19	12	228
15 - 19	12	10	120
20 - 24	7	13	91
25 - 34	9	18	162
Total	60		659.5

Mean = ∑f*m/∑f = 659.5/60 = 10.99

Mode = Maximum frequency interval = 10-14. Hence Mode lies in the interval 10-14

Marks	Frequency (f)	Cumulative Freq
0 - 9	13	13
10-14'	19	32
15 - 19	12	44
20 - 24	7	51
25 - 34	9	60
Total	60

Half of Total Freq = 60/2 = 30

Hence Median (Q) will lie in the interval 10-14

Hence,

{(Q – 10) / (30-13)} = {(14-10) / (32-13)}

Hence, Q = 13.58

Hence, Median = 13.58

c)

Q1 or First Quartile.

Hence, 0.25*60 = 15^th Value. This lies in the range 10-14

Hence,

{(Q1 – 10) / (15-13)} = {(14-10) / (32-13)}

Hence, Q1 = 10.42

Similarly,

Q3 or Third Quartile.

Hence, 0.75*60 = 45^th Value. This lies in the range 20-24

Hence,

{(Q3 – 20) / (45-44)} = {(24-20) / (51-44)}

Hence, Q3 = 20.57

So, IQR = Q3 – Q1 = 20.57 – 10.42 = 10.15

d)

i)

Mean of Sample B = 2 * Mean of Sample A = 2 * 25 = 50 kg

ii)

Let Sample size of B be x

Then Sample size of A = 3x

Hence, 4x = 40 or x = 15

So,

Sample Size of B = 15

Sample Size of A = 3*15 = 45

iii)

Summation of X variables of A = Mean of Sample A * Sample Size of A = 25*45 = 1080

Summation of X variables of B = Mean of Sample B * Sample Size of B = 50*15 = 750

iv) We cannot calculate the Std Deviation without the individual values