The table below shows the frequency distribution of prices (in ₦) for tubers of yam sold in an agricultural market: | Price (₦) | Frequency (f) | | :--- | :--- | | 10 – 14 | 3 | | 15 – 19 | 5 | | 20 – 24 | 7 | | 25 – 29 | 3 | | 30 – 34 | 2 | What is the mean price of a tuber of yam?

The table below shows the frequency distribution of prices (in ₦) for tubers of yam sold i… — JAMB UTME

The table below shows the frequency distribution of prices (in ₦) for tubers of yam sold in an agricultural market:

Price (₦)	Frequency ( $f$ )
10 – 14	3
15 – 19	5
20 – 24	7
25 – 29	3
30 – 34	2

What is the mean price of a tuber of yam?

A
₦19
₦21Cevap
C
₦22
D
��23

Cevap

The mean price of a tuber of yam is ₦21.

The mean price is calculated by multiplying each class interval midpoint by its frequency, adding these products together to obtain 420, and dividing by the total number of observations (20), giving ₦21.

Adım Adım Çözüm

Determine the midpoint (

x

) for each price class interval.

Class 10–14:

x = 12

; Class 15–19:

x = 17

; Class 20–24:

x = 22

; Class 25–29:

x = 27

; Class 30–34:

x = 32

Midpoints represent the central value of grouped class intervals.

Multiply each midpoint (

x

) by its corresponding frequency (

f

) to find

fx

, and sum all products (

\sum fx

\sum fx = (12 \times 3) + (17 \times 5) + (22 \times 7) + (27 \times 3) + (32 \times 2) = 36 + 85 + 154 + 81 + 64 = 420

Weighting midpoints by frequency gives the total aggregate value.

Sum the total frequencies (

\sum f

) and calculate the mean (

\bar{x} = \frac{\sum fx}{\sum f}

\sum f = 3 + 5 + 7 + 3 + 2 = 20

. Therefore,

\bar{x} = \frac{420}{20} = 21

The grouped mean is total aggregate value divided by total number of items.

Anahtar Kavram

Calculation of the Arithmetic Mean from Grouped Frequency Data

Soru

Cevap

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