Statistical Tools and Interpretation Test

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Statistical Tools and Interpretation Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Which partition value divides the data into four equal parts contains approximately one-fourth of the total number of observations?

A
Deciles

B
Mode

C
Quartile

D
Percentile

Solution

Quartiles are the measures which divide the data into four equal parts and each part contains approximately (not necessarily exactly) one-fourth of the total number of observations, not necessarily equal in count. While quartiles aim to divide the data evenly, especially in larger datasets, it's important to note that in smaller datasets or datasets with repeated values, quartiles may not perfectly divide the data into equal counts.
Question 2
1 / -0

The most frequently occurring number in a set of values is called the:

A
Mode

B
Median

C
Mean

D
Range

Solution

The most frequently occurring number in a set of values is called the mode. The mode is indeed the value that appears most frequently in a data set. It is the value with the highest frequency, representing the peak of the frequency distribution.
Question 3
1 / -0

The arithmetic mean between \(\frac{x+a}{x}\) and \(\frac{x-a}{x}\) when \(x \neq 0\):

A
1

B
\(\frac{a}{x}\)

C
\(x\)

D
\(a\)

Solution

The arithmetic mean between two quantities \(=\frac{\frac{x+a}{x}+\frac{x-a}{x}}{2} \)
A. M. \(=\frac{x+a+x^2 a}{2 x} \)
A. M. \(=\frac{2 x}{2 x}=1\)
So, A.M. \(=1\)
Question 4
1 / -0

___________ is the half distance between the third and first quartiles.

A
Mean Deviation

B
Quartile Deviation

C
Variance

D
Standard deviation

Solution

Quartile Deviation (Q.D) is a measure of statistical dispersion, representing the semi-variation between the upper quartile (Q3) and the lower quartile (Q1) in a distribution. The formula for calculating the quartile deviation is:
\(Q.D=\frac{Q_3-Q_1}{2}\)
Question 5
1 / -0

A measure of central tendency useful for a shoe manufacture for knowing what size of shoes must be produced most is:

A
Median

B
Mean

C
Mode

D
Range

Solution

A manufacture would like to know the size of shoes which has maximum demand. Here mode is the most appropriate measure because it is repeated the highest number of times in the series.
Question 6
1 / -0

If X, M, Z are denoting mean, median and mode of a data and X : M = 9 : 8, then find the ratio M : Z.

A
5 : 4

B
7 : 6

C
8 : 9

D
4 : 3

Solution

Mode \(=3\) Median -2 Mean
\(\mathrm{Z}=3 \mathrm{M}-2 \mathrm{X}\)
Given,
\(\frac{X}{M}=\frac{9}{8}\)
\(X=\frac{9 M}{8}\)
Therefore,
\(Z=3 M-2 \times \frac{9 M}{8}=3 M-\frac{9 M}{4}\)
\(Z=\frac{3 M}{4}\)
Therefore,
\(\frac{M}{Z}=\frac{4}{3}\)
\(M: Z=4: 3\)

Question 7

1 / -0

The marks scored by 25 students in the exam are as follows. Find the average using assumed mean method.

Marks	50-60	60-70	70-80	80-90	90-100
Students	3	4	8	8	2

73.1

75.8

77.4

76.9 Solution

Marks	X = (Upper+ lower limit)/2	Students(F)	d = \(\frac{X-A}{c}\)	\(Fd\)
50-60	55	3	-20	-60
60-70	65	4	-10	-40
70-80	75=A	8	0	0
80-90	85	8	10	80
90-100	95	2	20	40
		\(\Sigma F =25\)		\(\Sigma Fd =20\)

Mean by Shortcut Method \(=A+\frac{F{d}}{\Sigma {F}}\)

\( =75+\frac{20}{25} \)

\( =75+\frac{4}{5} \)

\(=75+0.8 =75.8\)

Question 8
1 / -0

The mean of ten numbers is 58. If one of the numbers is 40, what is the mean of the other nine?

A
60

B
540

C
162

D
162

Solution

Mean is calculated as the sum of the values of all observations divided by the number of observations
Mean = 58, N= 10
sum of the values of all observations = 58 x 10 = 580
Corrected sum of the values of all observations = 580 - 40 = 540
Corrected number of observations = 10 – 1 = 9
Correct Mean = \(\frac{540}{9}\) = 60
Question 9
1 / -0

Which measure of central tendency includes the magnitude of scores?

A
Mean

B
Mode

C
Median

D
Range

Solution

The measure of central tendency that includes the magnitude of scores is the mean. The mean is calculated by summing up all the scores in a dataset and dividing by the total number of scores. It takes into account the magnitude of each individual score in the dataset.
Question 10
1 / -0

The monthly income of the of six families is given as:
\(1600, 1500, 1400, 1525, 1625, 1630\)
What will be the value of mean family income?

A
\(1547\)

B
\(2156\)

C
\(1654\)

D
\(3255\)

Solution

The mean family income is obtained by adding up the incomes and dividing by the number of families.
So, mean family income \( =\frac{1600+1500+1400+1525+1625+1630}{6} =\) Rs. \(1547\)

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Statistical Tools and Interpretation Test - 1

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Statistical Tools and Interpretation Test - 1

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SHARING IS CARING

Question 1

Deciles

Mode

Quartile

Percentile

Solution

Question 2

Mode

Median

Mean

Range

Solution

Question 3

1

\(\frac{a}{x}\)

\(x\)

\(a\)

Solution

Question 4

Mean Deviation

Quartile Deviation

Variance

Standard deviation

Solution

Question 5

Median

Mean

Mode

Range

Solution

Question 6

5 : 4

7 : 6

8 : 9

4 : 3

Solution

Question 7

73.1

75.8

77.4

76.9

Solution

Question 8

60

540

162

162

Solution

Question 9

Mean

Mode

Median

Range

Solution

Question 10

\(1547\)

\(2156\)

\(1654\)

\(3255\)

Solution

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