Math / Data & Statistics

QuestionMegan recorded the temperature in her garden each morning for 6 days.
The mean of her six recorded temperatures was $2.1^{\circ} \mathrm{C}$ . The temperature on one of the days was $4.1^{\circ} \mathrm{C}$ .
What was the mean of her other 5 recorded temperatures? Give your answer as a decimal.

Studdy Solution

STEP 1

1. Megan recorded temperatures for 6 days.
2. The mean of the 6 recorded temperatures is $2.1^\circ \mathrm{C}$ .
3. One of the temperatures recorded was $4.1^\circ \mathrm{C}$ .

STEP 2

1. Calculate the total sum of the 6 recorded temperatures.
2. Subtract the known temperature from the total sum to find the sum of the other 5 temperatures.
3. Calculate the mean of the other 5 temperatures.

STEP 3

Use the formula for the mean to find the total sum of the 6 temperatures:
$\text{Mean} = \frac{\text{Total Sum of Temperatures}}{\text{Number of Temperatures}}$
Given that the mean is $2.1^\circ \mathrm{C}$ and there are 6 temperatures:
$2.1 = \frac{\text{Total Sum}}{6}$
Multiply both sides by 6 to find the total sum:
$\text{Total Sum} = 2.1 \times 6 = 12.6$

STEP 4

Subtract the known temperature from the total sum to find the sum of the other 5 temperatures:
$\text{Sum of Other 5 Temperatures} = 12.6 - 4.1 = 8.5$

STEP 5

Calculate the mean of the other 5 temperatures:
$\text{Mean of Other 5 Temperatures} = \frac{\text{Sum of Other 5 Temperatures}}{5} = \frac{8.5}{5} = 1.7$
The mean of her other 5 recorded temperatures is:
$\boxed{1.7}$

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