# Free Statistics 03 Practice Test - 10th Grade

The median for grouped data is formed by using the formula:

A.

l+(n2cff ) ×h

B.

l(n2cff ) ×h.

C.

l+(n2+cff ) ×h.

D.

l+2n

#### SOLUTION

Solution : A

The median for grouped data is formed by l+(n2cff ) ×h.

Where l is lower class limit of median class.
n is total number of observations.
cf is the cumulative frequency of the class preceding the median class.
f is the frequency of the median class and h is the class size.

The following data shows monthly savings of 100 families . Calculate the mode of the given frequency distribution.

Monthly savings(Rs)                Number of families        10002000142000300015300040002140005000275000600025

A.

4790

B.

4760

C.

4750

D.

4780

#### SOLUTION

Solution : C

Modal class is 4000-5000 within

f1 = 27, f0 = 21, f2 = 25, I = 4000, h = 1000

Mode = l + f1f02f1f0f2×h

Mode = 4000 + 68×1000

= 4750

Find the mode of the following data.

Class interval0100100200200300300400400500Frequency7111598

___

#### SOLUTION

Solution :

Modal Class is 200-300

Mode=I+(f1f02f1f0f2)×h

=200+151130119×100=240

The below table shows that profit made by a group of shops in mall. Then the median is _____.

Profit per shop less than (%)102030405060No. of shops1230577794100

A.

27.4

B.

31.2

C.

26.8

D.

23.7

#### SOLUTION

Solution : A

Firstly, the cumulative frequency (CF) table is drawn.

C.ICFFrequency01012121020301820305727304077204050941750601006Total100

n2=1002=50

C.F  nearest to 50 and greater than 50 is 57.

Median=l+(n2cff)×h
Where l is lower class limit of median class.
n is total number of observations.
cf is the cumulative frequency of the class preceding the median class.
f is the frequency of the median class and h is the class size.
Median=20+(503027)×10

Median = 27.4

The times (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated below

Class13.8141414.214.214.414.414.614.614.814.815Frequency245714820

The number  of atheletes who completed the race in less than 14.6 s is

A.

11

B.

71

C.

82

D.

130

#### SOLUTION

Solution : C

The number of atheletes who completed the race in less than 14.6

= 2 + 4 + 5 + 71

= 82

In the assumed mean method, if A is the assumed mean, then deviation di is :

A. xiA
B. xi+A
C. xi
D. Axi

#### SOLUTION

Solution : A

The deviation is di=xiA

In the assumed mean method, if A is the assumed mean, then deviation di is :

A.

xiA

B.

xi+A

C.

xi

D.

Axi

#### SOLUTION

Solution : A

In statistics, 'the assumed mean' is a method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand.

During the application of the short-cut method for finding the mean, the deviation d, are divisible by a common number ‘h’. In this case, the di = xi – A is reduced to a great extent as 'di' becomes dih. In this method, we divide the deviations by the same number to simplify calculations. The deviation is di=xiA

For which data set, the mean is not a good representative measures of central tendency.

A. There are 7 classes with the below frequencies.

{10, 12, 15, 17, 14, 15, 17}
B. There are 6 classes with the below frequencies.

{2, 20, 25, 17, 19, 22}
C. There are 7 classes with the below frequencies.

{5, 7, 5, 6, 4, 5, 7}
D. There are 6 classes with the below frequencies.

{17, 20, 25, 17, 19, 22}

#### SOLUTION

Solution : B

We know that extreme values in the data affect the mean. Here only for the data set {2, 20, 25, 17, 19, 22}, we find the extreme value as one class has the frequency as 2 and the others have frequency 20, 25, 17, 19 and 22.

The following table gives the life time of 200 neon lamps. Find the median class. A. 2500 - 3000
B. 1000 - 1500
C. 1500 - 2000
D. 3000 - 3500

#### SOLUTION

Solution : A The median class is identified as the class whose cumulative frequency  will be greater than n2, where 'n' is the sum of  the frequencies. (n=200).
Next, we divide 200 by 2.

n2=2002=100

We now locate the class whose cumulative frequency is greater than 100.
"2500 - 3000" is the class whose cumulative frequency 155 is greater than 100.
The median class is 2500 - 3000. A.  1 - 2
B. 2 - 3
C.  6 - 7
D.  7 - 8

#### SOLUTION

Solution : B

Here we locate a class with the maximum frequency. From the given table we find the maximum frequency as 12 whose class is 2 - 3. Therefore the modal class is 2 - 3.