Descriptive statistics

PROBLEMS

"Study little but study very thoroughly, because it is thoroughness in work which pays in the long run."

Q1

If there are 7 observations

4,6,8,12,10,20,24,

then the sum of deviation of the

observations from their AM is ?

( ) ?x x- =å

Q2

If a variable assumes the values

1,2, 3 ... 5

with frequencies as

1, 2, 3 ... 5,

then what is the AM?

Q3

The average salary of a group of

unskilled workers is Rs.10000

and that of a group of

skilled workers is Rs.15,000.

If the combined salary is Rs.12000, then what is the percentage of skilled workers?

Q4

The weighted arithmetic mean of the four numbers

26, 128, 12 and 4 is 10.4.

If the weights of the first three numbers are 1, 3 and 4

respectively, find the weight of the

fourth number?

Q5

The weighted AM of

3, 5 and 10

with weights

x, y and z

respectively is known to be 8.

What is the weighted AM if the weights are changed to 2x, 2y and 2z respectively?

Q6

The algebraic

sum of the deviations

of 25 observations measured from 45

is – 55

find the A.M. of the observations?

Q7

The weighted arithmetic mean of

first n natural numbers

whose weights are equal to the corresponding numbers is equal to?

Q9

The average weight of the following frequency distribution is 17.

Find the value of p

X 8 20 26 29

F 3 2 p 1

Q10

The mean age of a group of 50 persons was found to be 48 Later, it was discovered

that age 40,34,56 was misread as 30,43,52 Then the correct mean is?

Q11

The numbers

3.2, 5.8, 7.9 and 4.5

have frequencies

x, x+2, x–3 and x+6

respectively, If the arithmetic mean is 4.876, find the value of x?

Q13

What is the GM for the numbers 8, 24 and 40?

If A.M. = 25; H. M. = 9, then GM =? Calculate geometric mean of the four numbers

5,8,6,1 with frequency

3,2,4,1

Q14

If the AM of two unequal positive real nos

a and b (a>b)

be twice as that of its GM for two numbers then the

ratio a : b ?

Q15

If there are two groups with

75 and 65

as harmonic means and containing

15 and 13

observation then find the

combined HM ?

Q16

An, aero plane flies from

A to B

at the rate of 500 km/hour and comes back from B to A

at the rate of 700 km/hour.

The average speed of the aero plane is?

Q17

A motor car covered a distance of

50 miles

four times

The first time at 50 mph, the second at 20 mph, the third at 40 mph and the fourth

at 25 mph.

Calculate the average speed.

Q18

“MOI” travelled some distance by cycle at a speed of 15 km per hour.

On return journey he travelled the same distance at a speed of 10 km per hour.

What was his

average speed per hour during the entire journey?

Q19

Find the Harmonic mean of the following numbers: 1,

Find the Harmonic mean of the following numbers:

1 1 1, ,........, .2 3 n

1 1 11, , ,......,3 5 2 1n

Q20

What is the H.M of the following data relating to the age distribution of 72

persons?

Age (Year): 20 30 40

No. of people: 13 28 31

Q21

Find the H.M of the following data

Class Frequency 10 – 15 4

15 – 20 8 20 – 25 12 25 – 30 20 30 – 35 11

35 – 40 6 40 – 45 5

Q22

The median of the following observation

22,24,33,37,x+1,x+3,44,47,51,58

arranged in ascending order is 42

find x?

Q23

You are given below a certain statistical distribution. Calculate the most suitable

average.

Value FrequencyLess than 100 40

100 – 200 89 200 – 300 148 300 – 400 64

400 and above 39

Q24

If x and y are related by

2x – ½y =10

and mode of x is known to be 7.5,

then the mode of y is?

Q25

For the given data find the three quartiles23, 14, 24,45, 23, 34,43, 12, 34,45, 23, 23,45, 56, 43,

42

Q25

The average American spends $65.88 per month dinning out (the Des Moines register).

a sample 25 of young adults provided the following dining out expenditures( in dollars)

over the past month.

253 101 245 467 131 0 225 80

113 69 198 95 129 124 11 178

104 161 0 118 151 55 152 134 169

ANSWER THE FOLLOWING?

1. COMPUTE THE MEAN MEDIAN AND MODE.2. CONSIDERING THE RESULTS ABOVE DO THESE

YOUNG SEEM TO SPEND ABOUT SAME AS AN AVERAGE AMERICAN EATING OUT.

3. COMPUTE THE FIRST AND THIRD QUARTILE.4. COMPUTE THE RANGE AND THE I.Q.R.

5. COMPUTE THE VARIANCE AND THE SATANDRAD DEVIATION.

6. THE SKEWNESS MEASURE FOR THE DATA IS -1.54?

7. CHECK THE ACCURACY OF THE ABOVE STATEMENT.

Q26

Find the standard deviation of first n natural numbers?

If the quartile DEVIATION is 30 and median 22, find the coefficient of quartile

deviation, assuming the distribution to be symmetrical.

Q27

The quartile deviation of the following distribution is:

Weights (Kg) No. of men40 – 45 1045 – 50 2250 – 55 2855 – 60 2060 – 65 1265 – 70 8

Q28

If the relation between x and y is 5y – 3x =10 and the mean deviation about mean for x is 12, then the mean deviation of y about

mean is?

Karl Pearson coefficient of skewness is 0.32.

Its standard deviation is 6.5 & mean is 29.6, find the mode and median?

Q29

What is the value of

mean deviation about mean

for the following observations?

50, 60, 50, 50, 60,

60, 60, 50, 50, 50,

60, 60, 60, 50.

Q30

The mean deviation about mode

for the numbers 4/11, 6/11, 8/11, 9/11, 12/11, 8/11

If the SD of the 1st n natural numbers is 2, then the value of n must be?

Q31

Prices of a particular commodity in five years in two cities are given below. Find from the data the city which had more stable prices

Prices in city A Prices in city B20 1022 2019 1823 1226 15

Q32

What is the standard deviation from the following data relating to the age distribution of 200

persons?

Age (Year): 20 30 40 50 60 7080

No. of people: 13 28 31 46 39 2320

Q33

The mean and SD

of a sample of 100 observations

were calculated as 40 and 5.1 respectively by a CA student who took one

observations as 50 instead of 40 by mistake.

The correct value of SD would be?

Q34

The standard deviation calculated from a set of 32 observations is 5.

If the sum of the observations is 80,

what is the

sum of the squares

of these observations?

Q35

For a group containing

100

observations,

the A.M. and S.D. were 8 and 10.

For 50 observations selected from these 100 observations the

A.M and S.D are 10 and 2 respectively.

Find the A.M. and S. D. of the other half.

Q36

Find the coefficient of variation of the following data:

Marks No of Students

0 – 10 4

10 – 20 10

20 – 30 16

30 – 40 12

40 – 50 8

Q37

The following data relates to the salary of workers of two factories

Factory A Factory B

No. of workers 80 110

Mean Rs 2320 Rs 2160

SD Rs 120 Rs 122

In which factory is variation in salary more?

Q38

For 2 values of a variable x,

the mean and the standard deviation

are 10 and 2

respectively.

What are the values of x?

Q39

For a set of ungrouped values the following sums are found:

N = 15,

= 480,

= 15735.

Find the mean and standard deviation

of the values.

Xå2

Xå

Q40

The INTER QUARTILE RANGE of the following distribution is:

Weights (Kg) No. of men400–450 10450–500 22500–550 28550–600 20600–650 12

650–700 8

Q42Wageweb conducts surveys of salary data and present

the summaries on its website. Assume the following data come from a sample of annual salaries for 20

marketing executives (data are in thousands)

145,140,145,173,116,127,155,134,138,

114,951,621,271,131,781,439,316,516,157

184CALCULATE PEARSON COEFFICENT?

Q43

Find mean deviation and its coefficient for the data

wages No of workers

0 – 1000 4

1000 – 2000 10

2000 – 3000 16

3000 – 4000 12

4000– 5000 8

Q45

Prove that the

standard deviation

calculated from two values

a and b

is equal to half of their difference

Q46The following table gives the earned run averages (eras) for the

2002 season for the pitching staffs of the 16 baseball teams in the national league.

Arizona 3.92 Milwaukee 4.73

Atlanta 3.13 Montreal 3.97

Chicago 4.29 New York 3.89

Colorado 5.20 Philadelphia 4.17

Cincinnati 4.27 Pittsburgh 4.23

Florida 4.36 St. Louis 3.70

Houston 4.00 San Diego 4.62

Los Angeles 3.69 San Francisco 3.54

CALCULATE

mean (eras) median and mode variance of the data standard deviation and its coefficient comment on skewness of the data calculate I.Q.R

ANALYSEYou are given the data of a factory before and after the

settlement of industrial dispute.

comment on the gain or losses from the point of the workers and the management

BEFORE AFTER

NO OF WORKERS

2440 2359

MEAN WAGES 45.5 47.5

MEDIAN WAGES 49.0 45.0

STANDARD DEVIATION

12.0 10.0

ANALYSEFrom the data given below state Which series is more

consistent?

Variable Series A Series B

10-20 20 13

20-30 18 22

30-40 32 40

40-50 40 32

50-60 22 18

60-70 18 10