Certainly! Let's go through each part of the question systematically.
### 1.1 Modal Number of Sweets in a Packet
To find the mode, we need to identify the number that appears most frequently in the data set. The data set is:
[tex]\[ 24, 26, 26, 27, 20, 20, 20, 20, 20, 21, 55, 56, 67, 0, 11, 24, 55, 56, 67, 0, 11, 24, 55, 56, 67 \][/tex]
From this list, we can see that the number 20 appears most frequently (5 times).
Mode: 20
### 1.2 Determining the Measures of Spread
### 1.2.1 Median
To find the median, we first need to sort the data and then find the middle number. The sorted data set is:
[tex]\[ 0, 0, 0, 11, 11, 20, 20, 20, 20, 20, 21, 24, 24, 24, 26, 26, 27, 55, 55, 55, 56, 56, 56, 67, 67 \][/tex]
Since there are 25 numbers (an odd number of data points), the median will be the 13th number in this sorted list since it is an odd-number of data points:
Median: 24.0
### 1.3 Calculate the Range
The range is the difference between the highest and lowest values in the data set. From the sorted list:
[tex]\[ \text{Highest value} = 67 \][/tex]
[tex]\[ \text{Lowest value} = 0 \][/tex]
Range = Highest value - Lowest value = 67 - 0 = 67
### 1.4 Percentage of Packets with Sweets Above the Upper Quartile
The upper quartile (Q3) is the value below which 75% of the data falls. To find this, we need to determine the value at the 75th percentile of the sorted data set.
In this sorted list of 25 data points, the position of the upper quartile is [tex]\(\frac{75}{100} \times 25 = 18.75\)[/tex]
Since 18.75 is not a whole number, we take the average of the 18th and 19th data points in the sorted list. Both of these data points are 55.
Upper quartile (Q3): 55
Next, we count the number of data points that are greater than 55. Looking at the sorted list:
[tex]\[ 56, 56, 56, 67, 67 \][/tex]
There are 5 data points above 55 out of the total 25 data points. Therefore, the percentage of packets with sweets above the upper quartile is:
[tex]\[ \left(\frac{5}{25}\right) \times 100 = 20\% \][/tex]
Percentage of packets with sweets above the upper quartile: 20.0%
### Summary
1. Modal number of sweets in a packet: 20
2. Median number of sweets in a packet: 24.0
3. Range of the number of sweets in a packet: 67
4. Percentage of packets with sweets above the upper quartile: 20.0%
