Question

The histogram below shows information about the

daily energy output of a solar panel for a number of
days.
Calculate an estimate for the mean daily energy
output.
If your answer is a decimal, give it to 1 d.p.
Frequency density
5↑
t
W
2
1
1 2
3
4
5
6
Energy output (kWh)
7 8
a

Answer 1

To estimate the mean daily energy output from the given histogram, we need to calculate the midpoint of each bar and then find the average of those midpoints.

Looking at the histogram, we can approximate the midpoints as follows:

Midpoint of first bar (2-3): (2 + 3) / 2 = 2.5
Midpoint of second bar (3-4): (3 + 4) / 2 = 3.5
Midpoint of third bar (4-5): (4 + 5) / 2 = 4.5
Midpoint of fourth bar (5-6): (5 + 6) / 2 = 5.5
Midpoint of fifth bar (6-7): (6 + 7) / 2 = 6.5
Midpoint of sixth bar (7-8): (7 + 8) / 2 = 7.5

Now, let's calculate the weighted sum of the midpoints, considering the frequency density of each bar:

(2.5 * 5) + (3.5 * 2) + (4.5 * 1) + (5.5 * 4) + (6.5 * 8) + (7.5 * 5)

= 12.5 + 7 + 4.5 + 22 + 52 + 37.5

= 135.5

The sum of the frequency densities is 5 + 2 + 1 + 4 + 8 + 5 = 25.

To find the mean daily energy output, we divide the weighted sum by the sum of the frequency densities:

Mean daily energy output = 135.5 / 25

≈ 5.42 kWh (rounded to 1 decimal place)

Therefore, the estimated mean daily energy output is approximately 5.4 kWh.