The mean of eight consecutive odd numbers is 24. What is the median of the first four numb… — JAMB UTME

The mean of eight consecutive odd numbers is $24$ . What is the median of the first four numbers?

Answer: 20

The median of the first four numbers is

20

Letting the eight consecutive odd numbers be

x, x+2, \dots, x+14

, their sum is

8x + 56

. Dividing by

8

gives a mean of

x + 7 = 24

, so

x = 17

. The first four numbers are

17, 19, 21,

and

23

. The median of these four values is the average of the middle two values (

19

and

21

), which equals

20

Represent the eight consecutive odd numbers algebraically

Let the numbers be

x, x+2, x+4, x+6, x+8, x+10, x+12, x+14

Consecutive odd numbers increase by steps of

2

Set up and solve the mean equation

\frac{(x) + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) + (x+12) + (x+14)}{8} = 24 \implies x + 7 = 24 \implies x = 17

The mean of ungrouped data is the sum of all data values divided by the total number of values.

Identify the first four numbers in the set

The first four numbers are

17, 19, 21, 23

Substitute

x = 17

into

x, x+2, x+4,

and

x+6

Find the median of the first four numbers

\text{Median} = \frac{19 + 21}{2} = 20

For an even count of ordered values (4 items), the median is the arithmetic mean of the two middle terms.

Measures of Central Tendency for Ungrouped Data

Question