Question

this list shows how many hours twenty batteries lasted when they run continually in a flashlight. 78 51 47 31 16 58 30 10 60 40 63 65 93 13 93 22 64 47 10 46 what is the mean, median, and mode of the battery life data? a. mean: 47 median: 46.85 mode: 10, 47, 93 b. mean: 46.85 median: 47 mode: 10, 47, 93 c. mean: 46.85 median: 47 mode: none d. mean: 47 median: 46.85 mode: none please select the best answer from the choices provided.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 20$ and $x_{i}$ are the data - points.
$\sum_{i=1}^{20}x_{i}=16 + 51+47+31+78+40+30+10+60+58+93+10+65+63+46+93+64+47+13+22=937$
$\bar{x}=\frac{937}{20}=46.85$

Step2: Arrange data in ascending order

$10,10,13,16,22,30,31,40,46,47,47,47,51,58,60,63,64,65,93,93$

Step3: Calculate the median

Since $n = 20$ (even), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered data points.
The 10 - th value is 47 and the 11 - th value is 47. Median $=\frac{47 + 47}{2}=47$

Step4: Calculate the mode

The mode is the data - point that appears most frequently. The number 47 appears 3 times and 93 appears 2 times, and other numbers appear less frequently. So the mode is 47.

Answer:

C. mean: 46.85, median: 47, mode: 47