Step 1a

To find the mean absolute deviation:
Calculate the mean (average) temperature:

\$"Mean" = (20 + 22 + 18 + 23 + 21 + 19 + 25) / 7\$
​⇒ \$148 / 7\$
⇒ 21.14

Absolute deviation:
\$\∣ 20 − 21.14\∣ = 1.14\$
\$\∣22 − 21.14\∣ = 0.86\$
\$\∣18 − 21.14\∣ = 3.14\$
\$\∣23 − 21.14\∣ = 1.86\$
\$\∣21 − 21.14\∣ = 0.14\$
\$\∣19 − 21.14\∣ = 2.14\$
\$\∣25 − 21.14\∣ = 3.86\$

Explanation: Here, we find the absolute deviation of each temperature. The mean temperature is 21.14.

Step 1b

Calculate the mean of these absolute deviations:

MAD = \$(1.14 + 0.86 + 3.14 + 1.86 + 0.14 + 2.14 + 3.86) / 7\$
⇒ \$13.14/7\$
⇒ 1.88

Explanation: Therefore, the mean absolute deviation of the temperatures is approximately 1.88° Celsius.

Step 2a

To find the standard deviation Calculate the mean (average) age:

Mean = \$(18 + 20 + 22 + 19 + 21 + 23 + 20)/7\$
⇒ \$143/7\$
⇒ 20.43

Squared deviation:
\$(18 − 20.43)^2\$ = 4.1849
\$(20 − 20.43)^2\$ = 0.1849
\$(22 − 20.43)^2\$ = 2.4649
\$(19 − 20.43)^2\$ = 2.0449
\$(21 − 20.43)^2\$ = 0.3364
\$(23 − 20.43)^2\$ = 6.7249
\$(20 − 20.43)^2\$ = 0.1849

Explanation: Here, we find the squared deviation of each age from the mean. The mean age is 20.43.

Step 2b

\$"Mean of Squared Deviations" = (4.1849 + 0.1849 + 2.4649 + 2.0449 + 0.3364 + 6.7249 + 0.1849) / 7\$

⇒ \$16.1257 / 7\$

⇒ 2.304

Take the square root of the mean of squared deviations to find the standard deviation:

\$"Standard Deviation" = \sqrt(2.304)\$

⇒ 1.52

Explanation: Here, we calculate the mean of these squared deviations. Therefore, the standard deviation of the ages is approximately 1.52.

Step 3a

Percentage = \$("Number of Red Apples") / ("Total Numbers of Apples") \times 100\$

Percentage = \$8/20 \times 100\$

Percentage = \$0.4 \times 100\$

Percentage = 40%

Explanation: Therefore, 40% of the apples in the basket are red.