The following outcomes were recorded when a dice was thrown 30 times
2,3,5,4,4,3,5,1,4,3,1,1,4,2,3,5,1,4,2,2,3,2,1,5,5,2,1,3,5,1
a. Prepare the frequency table for the data above
b.find the mean of the data
c.find the mode
a. Frequency table:
Number | Frequency
-------|----------
1 | 7
2 | 6
3 | 5
4 | 6
5 | 6
b. Mean:
To find the mean, add up all the numbers and divide by the total number of throws:
(2+3+5+4+4+3+5+1+4+3+1+1+4+2+3+5+1+4+2+2+3+2+1+5+5+2+1+3+5+1) / 30
= 93 / 30
= 3.1
So the mean is 3.1.
c. Mode:
The mode is the most commonly occurring number, which in this case is 1 (which occurred 7 times). So the mode is 1.
a. To prepare the frequency table for the given data, first, let's list all the unique outcomes along with the frequency (number of occurrences) of each outcome.
Outcome | Frequency
---------|----------
1 | 6
2 | 6
3 | 6
4 | 5
5 | 7
b. To find the mean of the data, we need to calculate the sum of all the outcomes and divide it by the total number of outcomes.
Sum of outcomes = 2 + 3 + 5 + 4 + 4 + 3 + 5 + 1 + 4 + 3 + 1 + 1 + 4 + 2 + 3 + 5 + 1 + 4 + 2 + 2 + 3 + 2 + 1 + 5 + 5 + 2 + 1 + 3 + 5 + 1 = 95
Number of outcomes = 30
Mean = Sum of outcomes / Number of outcomes = 95 / 30 = 3.17 (rounded to two decimal places)
c. To find the mode, we need to identify the outcome(s) that occur most frequently.
From the frequency table calculated in part a, we can see that the outcomes 1, 2, and 3 all occur 6 times, which is the maximum frequency. Therefore, the mode(s) of the data are 1, 2, and 3.