Measures of Central Tendency - Online Test
Q1. What is the median of the following set of scores? 19, 5, 12, 10, 14?
Answer : Option D
Explaination / Solution:
Arranging the data, in ascending order, Median = size of (N+1)/2 item i.e. 12 .
Q2. Approximately what percentage of scores falls within one standard deviation of the mean in a normal distribution?
Answer : Option C
Explaination / Solution:
No Explaination.
Q3. Suppose a researcher is concerned with a nominal scale that identifies users versus nonusers of bank credit cards. The measure of central tendency appropriate to this scale is the
Answer : Option C
Explaination / Solution:
Here, Mode is the most appropriate measure. Mode is the most frequently observed data value.
Q4. What is the mean of this set of numbers: 4, 6, 7, 9, and 2000000?
Answer : Option D
Explaination / Solution:
Arithmetic mean by direct method isthe sum of all observations in a seriesdivided by the total number ofobservations. Mean = 4+6+7+9+2000000 = 2000026/5= 400005.2
Q5. The mean of 11 numbers is 7. One of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?
Answer : Option C
Explaination / Solution:
Given Sum of all observations = 11x7=77
Correct Sum of all observations = 77-13 = 64
Correct total number of observations= 11-1= 10
Correct Mean = Correct Sum of all observations/ Correct total number of observations= 64/10 = 6.4
Q6. The mean of ten numbers is 58. If one of the numbers is 40, what is the mean of the other nine?
Answer : Option B
Explaination / 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 = 540/9 = 60
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 = 540/9 = 60
Q7. A batsman scores the following number of runs in 6 innings: 36, 35, 50, 46, 60, and 55. Calculate the mean runs scored in an inning.
Answer : Option D
Explaination / Solution:
Mean is calculated as the sum of the values of all observations divided by the number of observations
N= 6
Sum of the values of all observations = 36+35+50+46+60+55 = 282
Mean = 282/6 = 47
N= 6
Sum of the values of all observations = 36+35+50+46+60+55 = 282
Mean = 282/6 = 47
Q8. If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Find the mean of 1st three observations
Answer : Option B
Explaination / Solution:
Mean is calculated as the sum of the values of all observations divided by the number of observations
N= 3
Sum of the values of 1st. three observations = 11+9+7= 27
Mean = 27/3 = 9
N= 3
Sum of the values of 1st. three observations = 11+9+7= 27
Mean = 27/3 = 9
Q9. The mean of 40 observations was 160. It was detected on re-checking that the value 165 was wrongly copied as 125 for computation of mean. Find the correct mean.
Answer : Option C
Explaination / Solution:
Mean is calculated as the sum of the values of all observations divided by the number of observations
N= 40 , Mean = 160
Sum of the values of all observations = 40 x 160 = 6400
Sum of the values of all observations after correction= 6400 -125 = 6275+165 = 6440
Correct Mean = 6440/40 = 161
N= 40 , Mean = 160
Sum of the values of all observations = 40 x 160 = 6400
Sum of the values of all observations after correction= 6400 -125 = 6275+165 = 6440
Correct Mean = 6440/40 = 161
Q10.
Find the median
Answer : Option D
Explaination / Solution:
In case of discrete series the position of median i.e. (N+1)/2th item can be located through cumulative frequency. The corresponding value at this position is the value of median.
Value: 20 29 30 39 44
Frequency: 2 4 4 3 2
Cumulative frequency 2 6 10 13 15
M= 15+1/2 = 8th place which is located in 30
Value: 20 29 30 39 44
Frequency: 2 4 4 3 2
Cumulative frequency 2 6 10 13 15
M= 15+1/2 = 8th place which is located in 30
