Alright, let's answer each part of the question one by one.
Given Data Set:
50, 36, 45, 36, 43, 56, 42, 44, 36
### (a) Calculate the Median
The median is the middle value in a data set when the numbers are arranged in ascending order. If the dataset has an odd number of observations, the median is the middle number. If it has an even number, the median is the average of the two middle numbers.
Here we have 9 numbers, which is odd. First, we sort the data in ascending order:
36, 36, 36, 42, 43, 44, 45, 50, 56
With 9 numbers, the median will be the 5th number (because [tex]\(\frac{9+1}{2} = 5\)[/tex]).
So, the median is the 5th number: 43.0
### (b) Calculate the Mean
The mean (average) is found by summing all the values and then dividing by the number of values.
Sum of all values:
[tex]\(50 + 36 + 45 + 36 + 43 + 56 + 42 + 44 + 36 = 388\)[/tex]
Number of values: 9
Mean = [tex]\(\frac{388}{9} = 43.1111...\)[/tex]
Rounded to one decimal place: 43.1
### (c) Calculate the Mode
The mode is the value(s) that appear most frequently in the data set.
From the data set:
36 appears 3 times,
50 appears 1 time,
45 appears 1 time,
43 appears 1 time,
56 appears 1 time,
42 appears 1 time,
44 appears 1 time.
Since 36 appears most frequently (3 times), it is the mode.
Number of modes: 1
Value of mode: 36
### Summary
- (a) Median: 43.0
- (b) Mean: 43.1
- (c) Modes:
- Number of modes: 1
- Value of modes: 36
