Test: Measures of Central Tendency - 1 - SSC CGL MCQ

Given:

Numbers: 10, 8, 2, 7, 3, 8, 5, 1

To find the median of a set of numbers, we arrange the numbers in ascending order and find the middle value. If the total number of values is odd, the median is the middle value. If the total number of values is even, the median is the average of the two middle values.

Calculation:

Arranging the numbers in ascending order:

⇒ 1, 2, 3, 5, 7, 8, 8, 10

F inding the median (k): Since the total number of values is 8, the median is the average of the two middle values:

⇒ (5 + 7) / 2 = 6.

Replacing 10 with 1 and arranging the new set of numbers in ascending order:

⇒ 1, 1, 2, 3, 5, 7, 8, 8

Finding the new median (r): Since the total number of values is still 8, the median is the average of the two middle values:

⇒ (3 + 5) / 2 = 4.

Calculating (k - r)

⇒ 6 - 4 = 2.

Therefore, the value of (k - r) is 2.

Given:

Three observations = x, y, z

Concept used:

The mean (average) of a set of observations is calculated by adding up all the observations and then dividing by the number of observations.

Calculation:

The mean (M) of these observations (x, y, z) is given by:

⇒ Mean = (x + y + z) / 3

∴ The mean of the three observations is (x + y + z) / 3.

The number which is occurred most frequently in a dataset is the mode in a data Set. A set of numbers can contain more than one Mode.

Where l = lower limit of median class,

n = number of observations,

h = class size, f = frequency of median class,

cf = cumulative frequency of class preceding the median class.
Calculation: 

From the given table we have formed the above table of cumulative frequency to find the median.

In the table, n = 150 + x + y = 150 + 78 = 228

which will lie between 42 + x and 107 + x,

therefore the median class: 40 - 50

l = 40, f = 65, cf = 42+x

The mean of 14, 13, 18, 16, k, (k + 3) = 13 which means

⇒ [14 + 13 + 18 + 16 + k + (k + 3)]/6 = 13

⇒ [ 2k + 64] = 78

⇒ k = 7

Then, the mean of k, 8, 9, 11, 5, 10, 6 is

⇒ [k + 8 + 9 + 11 + 5 + 10 + 6]/7 

⇒ [7 + 8 + 9 + 11 + 5 + 10 + 6]/7 

⇒ 56/7

⇒ 8

∴ The correct answer is 8

Mode in a data set is defined as the number that occurs most frequently in a data set.
5 occurred three times, 7 occurred two times, 2 and 21 occurred one time each.
5 is the most repeated number according to the definition mode.

Median

Cumulative frequency distribution is the sum of the frequency of class and all classes below it in a frequency distribution.

This means we can get cumulative frequency by adding up a value and all of the values that came before it.

Also,

Frequency of any class = cumulative frequency of class - cumulative frequency of preceding class.


l = lower limit of median class interval
cf = cumulative frequency preceding to the median class frequency
f = frequency of the class interval to which median belongs
h = width of the class interval

Here, the mean of 10 numbers is 96,

Then, total of the 10 members = 96 × 10 = 960

If one member is 150, then the total of  remaining 9 members = (960 - 150) = 810

Now, the mean of the remaining nine numbers = 810/9 = 90

∴ The correct answer is 90

90 occurred thrice. 77, 43 and 65 occurred twice.
In the above data set, 90 occurred three times and other numbers appeared once or twice. So, 90 is the mode of the above data set.

Concept:

Median: It is the middle value in the given set, while the set is either in increasing or decreasing order.

If the number of observation (n) is odd then median is (n+1)/2th term.

If the number of observation (n) is even then the median is average of nth and (n+1)th term.

 
Calculation:

Given data are 4.1, 5.2, 6.3, 3.6, 2.4, 6.4, 4.6

Increasing order of given data: 2.4, 3.6, 4.1, 4.6, 5.2, 6.3, 6.4

The number of observation is odd (n = 7)

So, the median is the  (n+1)/2th term or 4th term

Median is 4th term i.e., 4.6