Statistics Test

Result

Statistics Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Find median using an empirical relation when it is given that mean and mode are 12.5 and 9.8, respectively.

A
10.4

B
11.6

C
12.6

D
13.4

Solution

Given:
Mean = 12.5
Mode = 9.8

Empirical relation is,

3 Median = Mode + 2(Mean)
3 Median = 9.8 + 2(12.5)

3 Median = 9.8 + 25
3 Median = 34.8

Median = 34.8/3

Median = 11.6
Question 2
1 / -0

Out of 40 numbers, the mean of 15 observations is 18, and the mean of the remaining observations is 15. What is the mean of all 40 observations?

A
14.111

B
15.281

C
16.125

D
17.280

Solution

Total number of observations = 40
Mean of 15 observations = 18

Sum of 15 observations = 15 × 18 = 270
Mean of the rest of the observations = 15

Sum of rest of the observations = (40 - 15) × 15 = 25 × 15 = 375

Sum of all 40 observations = 270 + 375 = 645
Mean of 40 observations = 645 ÷ 40 = 16.125
Question 3
1 / -0

The mode of a frequency distribution with class intervals is found by using which type of graphical representation?

A
Ogives

B
Histogram

C
Circle graphs

D
Bar graph

Solution

In a specific data set, the mode can be defined as the value that has occurred most of the times. Mode is represented by histograms. The highest peak of the histogram represents the location of the mode of the data set.
Question 4
1 / -0

The average amount of money saved by Jasmine in 11 weeks is Rs. 1,650, out of which Rs. 1,500 is the average amount that she saved in 7 weeks and Rs. 1,780 is the average amount that she saved in the last 5 weeks. How much did she save in week 6 if she saved Rs. 1,000 more in week 6 than her savings of 7^th week?

A
Rs. 1,050

B
Rs. 1,250

C
Rs. 2,050

D
Rs. 2,250

Solution

Average (Mean) = Total amount saved ÷ Number of weeks
1,650 = Total amount saved ÷ 11
Total money saved by Jasmine in 11 weeks = Rs. 1,650 × 11 = Rs. 18,150

Total money saved in first 7 weeks = 1,500 × 7 = Rs. 10,500
Total money saved in last 4 weeks = Rs. 18,150 – 10,500 = Rs. 7,650

Total money saved in last 5 weeks = 1,780 × 5 = Rs. 8,900
Money saved in the 7^th week = Total money saved in last 5 weeks - Money saved in last 4 weeks = 8,900 – 7,650 = Rs. 1,250

Money saved in week 6 = 1,250 + 1,000 = Rs. 2,250