Find the mean,the median,and the mode of the observations:
$48, 41, 36, 35, 41, 37, 39, 52, 41, 48$
$48, 41, 36, 35, 41, 37, 39, 52, 41, 48$
(A) Step $1$: To find the mean,sum all observations and divide by the total count.
Sum $= 48 + 41 + 36 + 35 + 41 + 37 + 39 + 52 + 41 + 48 = 418$.
Total number of observations $n = 10$.
Mean $= \frac{418}{10} = 41.8$.
Step $2$: To find the median,arrange the data in ascending order:
$35, 36, 37, 39, 41, 41, 41, 48, 48, 52$.
Since $n = 10$ (even),the median is the average of the $5^{th}$ and $6^{th}$ terms.
Median $= \frac{41 + 41}{2} = 41$.
Step $3$: To find the mode,identify the observation that occurs most frequently.
The value $41$ appears $3$ times,which is more than any other value.
Mode $= 41$.
Sum $= 48 + 41 + 36 + 35 + 41 + 37 + 39 + 52 + 41 + 48 = 418$.
Total number of observations $n = 10$.
Mean $= \frac{418}{10} = 41.8$.
Step $2$: To find the median,arrange the data in ascending order:
$35, 36, 37, 39, 41, 41, 41, 48, 48, 52$.
Since $n = 10$ (even),the median is the average of the $5^{th}$ and $6^{th}$ terms.
Median $= \frac{41 + 41}{2} = 41$.
Step $3$: To find the mode,identify the observation that occurs most frequently.
The value $41$ appears $3$ times,which is more than any other value.
Mode $= 41$.
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