The frequency distribution table below shows the daily electricity consumption, in kilowat… — GRE General Test

The frequency distribution table below shows the daily electricity consumption, in kilowatt-hours ( $\text{kWh}$ ), recorded for a sample of $40$ small retail stores over a monitoring period.

Daily Electricity Consumption ( $\text{kWh}$ )	Number of Stores
$10 \le e < 30$	$6$
$30 \le e < 50$	$14$
$50 \le e < 70$	$12$
$70 \le e < 90$	$8$

Based on the table, what is the estimated mean daily electricity consumption, in $\text{kWh}$ , per store, using the midpoint of each interval to represent all data within that interval?

Cevap: 51 kWh

Cevap

To estimate the mean from grouped frequency data, each interval is represented by its midpoint. The midpoints for the four intervals are

20

40

60

, and

80

. Multiplying each midpoint by its frequency gives

20(6) = 120

40(14) = 560

60(12) = 720

, and

80(8) = 640

. The sum of these products is

120 + 560 + 720 + 640 = 2040

. Dividing this sum by the total frequency of

40

stores gives an estimated mean of

51\text{ kWh}

Adım Adım Çözüm

Determine the class midpoint for each interval of electricity consumption.

Midpoints:

\frac{10+30}{2} = 20

\frac{30+50}{2} = 40

\frac{50+70}{2} = 60

, and

\frac{70+90}{2} = 80

When working with grouped frequency data, each interval is represented by its midpoint value to estimate total sums.

Multiply each midpoint by the number of stores in that interval to find the estimated sum of consumption per group.

20 \times 6 = 120

40 \times 14 = 560

60 \times 12 = 720

80 \times 8 = 640

Weighting each midpoint by its interval frequency yields the total estimated consumption across all stores in that bin.

Sum the total estimated consumption across all intervals.

120 + 560 + 720 + 640 = 2040 \text{ kWh}

This calculation aggregate gives the total estimated electricity consumed by all 40 stores combined.

Divide the total estimated electricity consumption by the total number of stores.

\frac{2040}{40} = 51 \text{ kWh}

Dividing the aggregate total by the sample size gives the estimated arithmetic mean per store.

Anahtar Kavram

Calculating the estimated mean of grouped data using class midpoints and weighted frequencies.

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru