Numerical Ability Test - 32

Given:

Formula used:

Mean = (∑f_ix_i) / N

where f_i = frequency of i_th term

_Xi = i^th term

N = total observations

Calculations:

Mean = (∑f_ixi)/N

⇒ Mean = 661/27

⇒ Mean = 24.48

∴ The mean age of all patients is 24.48 years.

Since, 12, 16, k, 28, 32, 35, 39, 47, 53 are in ascending order

So, the value of k must be in between 16 to 28

∴ The value of k is 27 from option

GIVEN:

Data: 8, 7, 9, 14, 10, 6, 13, 8, 11, 7, 19, 12, 11, 7, 8, 10, 11, 14, 8, 10.

CONCEPT:

The mode is the number that appears most frequently in a data set.

CALCULATION:

Simply find the most recurring number:

8, 7, 9, 14, 10, 6, 13, 8, 11, 7, 19, 12, 11, 7, 8, 10, 11, 14, 8, 10

The most occurring number is 8 (4 times)

∴ Mode = 8

Given:

Mean = 21

Median = 19

Formula used:

Mean – Mode = 3(Mean – Median)

Calculation:

⇒ 21 – Mode = 3(21 – 19)

⇒ 21 – Mode = 3 × 2

⇒ 21 – Mode = 6

⇒ 21 – 6 = Mode

⇒ 15 = Mode

∴ The Mode is 15

GIVEN:

Lower limit of modal class = 3

Highest Number of families = 9

Class interval = h = 2

Frequency of modal class = f₁ = 9

Frequency of class before modal class = f₀ = 7

Frequency of class after modal class = f₂ = 2

FORMULAE USED:

Mode = L + (f₁ - f₀) × h/(2f₁ - f₀ - f₂)

CALCULATION:

Mode = 3 + (9 - 7) × 2/(18 - 7 - 2)

Mode = 3 + (4/9) = 3 + 0.444

∴ The mode of this data is 3.444

Given:

The following fractional numbers: 7/9, 13/16, 2/3, 21/25, 17/21

Formula used:

The median formula of a given set of numbers, say having 'n' odd number of observations, can be expressed as:

Median = [(n + 1)/2]^th term

The median formula of a given set of numbers say having 'n' even number of observations, can be expressed as:
Median = [(n/2)^th term + ((n/2) + 1)^th term]/2

Calculation:

7/9 = 0.77

13/16 = 0.81

2/3 = 0.66

21/25 = 0.84

17/21 = 0.80

Let,s arrange the series from smaller to greater numbers,

2/3, 7/9, 17/21, 13/16, 21/25

Here, n = 5 (odd)

Therefore, the middle term is 17/21.

∴​ The median of the following fractional numbers is 17/21

Given:

77, 5, 55, 29, 78, 27, 21, 19, 50, 19, 87, 33, 35, 75, 41

Concept used:

The range of a given data is the difference between the highest term of the data and the lowest term of the data

Calculations:

Given data = (77, 5, 55, 29, 78, 27, 21, 19, 50, 19, 87, 33, 35, 75, 41)

Highest term of the data = 87

Lowest term of the data = 5

Range = 87 - 5

⇒ 82

∴ The range of the given data is 82

Concept used:

The median is the middle value of a data set.

Calculation:

According to the given dataset, x + 2 is the middle value which is the median,

So, x + 2 = 21

⇒ x = 19

Then, the value of 3x + 7 = (3 × 19 + 7) = 64

∴ The correct answer is 64

Given:

Concept used:

Calculation:

So, mean = 433/20

⇒ 21.65

Now,

To find the mean deviation we have to construct another table

Formula used:

Mode is the value that appears most frequently in a data set.

Calculation:

The mode is the value with the highest frequency.

So, highest frequency (number of patients) = 7

Days of confinement with the highest frequency = 8

Thus, Mode = 8

∴ The correct answer is option (1).