Consider the following frequency distribution of daily sales for a shop that was kept for the months of
November and December in 2013.
Daily Sales ($) 60-70 70-80 80-90 90-100 100-110 110-120
Number of days 5 11 22 13 7 3
a. From this frequency distribution,
(i) draw a histogram. [4]
(ii) draw a frequency polygon . [4]
(iii) draw the corresponding ‘less than’ cumulative frequency curve. [5]
(iv) calculate the mode. [4]
(v) calculate the median and state how it compares with the estimate from part (d). [5]
b. Using the ogive in part a(iii) above, estimate the median daily sales for this shop. [4]
i have ansewered
To answer the question, you'll need to follow these steps:
Step 1: Create a histogram using the given frequency distribution.
- A histogram is a graphical representation of the distribution of data.
- To create a histogram, you need to plot the frequency on the y-axis and the daily sales ranges on the x-axis.
- Use a bar to represent each range, and the height of the bar should correspond to the frequency.
Step 2: Create a frequency polygon using the same frequency distribution.
- A frequency polygon is a line graph that displays the frequencies of different values or ranges.
- Start by plotting the midpoints of each range on the x-axis and the corresponding frequency on the y-axis.
- Connect the plotted points with line segments to form a polygon.
Step 3: Create a cumulative frequency curve ("less than" curve) using the cumulative frequency.
- To create the cumulative frequency curve, first calculate the cumulative frequency for each range.
- Start with the first frequency and add it to the next frequency as you move along.
- Plot the cumulative frequency on the y-axis and the upper limit of each range on the x-axis.
- Connect the points with line segments to form the curve.
Step 4: Calculate the mode.
- The mode represents the value that appears most frequently in the data.
- Look for the range with the highest frequency in the given frequency distribution to identify the mode.
Step 5: Calculate the median and compare it to the estimate from part (d).
- The median is the middle value in a set of data when it is arranged in ascending order.
- To calculate the median, you can use the cumulative frequency curve.
- Find the point on the x-axis that corresponds to the cumulative frequency closest to half of the total frequency. The corresponding value is the median.
- Compare this result to the estimate from part (d) to see if they are similar.
Step 6: Use the ogive (cumulative frequency curve) from part a(iii) to estimate the median daily sales for the shop.
- Use the cumulative frequency curve to find the point on the x-axis that corresponds to the cumulative frequency closest to half of the total frequency.
- The corresponding value on the x-axis is the estimated median daily sales for the shop.
Following these steps will allow you to answer all the questions and complete the task.