Question

1. the following data set represents the number of dollars 20 customers withdrew at an atm.

number of dollars	20	40	60	80	100	120
frequency	10	5	2	1	2	0

mean: ______ median: ______

Explanation:

Step1: Calculate the sum of the products of values and frequencies

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$.
$x_1 = 20,f_1=10$; $x_2 = 40,f_2 = 5$; $x_3=60,f_3 = 2$; $x_4 = 80,f_4=1$; $x_5 = 100,f_5=2$; $x_6 = 120,f_6 = 0$.
$\sum_{i = 1}^{6}x_{i}f_{i}=20\times10 + 40\times5+60\times2 + 80\times1+100\times2+120\times0=200+200 + 120+80+200+0=800$.

Step2: Calculate the total frequency

$\sum_{i = 1}^{6}f_{i}=10 + 5+2+1+2+0=20$.

Step3: Calculate the mean

$\bar{x}=\frac{800}{20}=40$.

Step4: Calculate the median

The total number of data points $n = 20$ (an even - numbered data set).
First, find the cumulative frequencies:
For $x = 20$, cumulative frequency $CF_1=10$; for $x = 40$, $CF_2=10 + 5=15$; for $x = 60$, $CF_3=15+2 = 17$; for $x = 80$, $CF_4=17 + 1=18$; for $x = 100$, $CF_5=18+2=20$.
The median is the average of the $\frac{n}{2}=10$th and $(\frac{n}{2}+1)=11$th ordered data values.
The 10th and 11th values fall within the group with $x = 40$. So the median is 40.

Answer:

Mean: 40
Median: 40