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Math  /  Data & Statistics

QuestionSeries 1 b) Define Histogram. Draw a histogram for the following frequency distribution: \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline X & 32 & 37 & 42 & 47 & 52 & 57 & 62 & 67 \\ \hline f & 3 & 17 & 28 & 47 & 54 & 31 & 14 & 4 \\ \hline \end{tabular}
Answer:

Studdy Solution

STEP 1

1. A histogram is a graphical representation of the distribution of numerical data, typically using bars to represent the frequency of numerical bins.
2. The provided frequency distribution consists of data points XX and their corresponding frequencies ff.
3. The histogram will use the values of XX as the midpoints of the bins and the values of ff as the heights of the bars.

STEP 2

1. Define the bins for the histogram based on the given XX values.
2. Plot the histogram using the bins and their corresponding frequencies.

STEP 3

Define the bins for the histogram. Since XX values are given, we will assume each value is the midpoint of a bin. Therefore, we need to determine the bin ranges. For simplicity, we can assume each bin spans halfway to the next midpoint.
For instance, the first bin spans from: [32−37−322,32+37−322]=[29.5,34.5] \left[ 32 - \frac{37-32}{2}, 32 + \frac{37-32}{2} \right] = \left[ 29.5, 34.5 \right]
Similarly, calculate the bin ranges for all XX values.

STEP 4

Calculate the bin ranges for each XX value:
Bin 1:[29.5,34.5]Bin 2:[34.5,39.5]Bin 3:[39.5,44.5]Bin 4:[44.5,49.5]Bin 5:[49.5,54.5]Bin 6:[54.5,59.5]Bin 7:[59.5,64.5]Bin 8:[64.5,69.5] \begin{aligned} & \text{Bin 1:} \quad [29.5, 34.5] \\ & \text{Bin 2:} \quad [34.5, 39.5] \\ & \text{Bin 3:} \quad [39.5, 44.5] \\ & \text{Bin 4:} \quad [44.5, 49.5] \\ & \text{Bin 5:} \quad [49.5, 54.5] \\ & \text{Bin 6:} \quad [54.5, 59.5] \\ & \text{Bin 7:} \quad [59.5, 64.5] \\ & \text{Bin 8:} \quad [64.5, 69.5] \\ \end{aligned}

STEP 5

Plot the histogram using the bins and their corresponding frequencies. For each bin, draw a bar with the bin range on the horizontal axis and the frequency on the vertical axis.
Bin RangeFrequency[29.5,34.5]3[34.5,39.5]17[39.5,44.5]28[44.5,49.5]47[49.5,54.5]54[54.5,59.5]31[59.5,64.5]14[64.5,69.5]4\begin{array}{|c|c|} \hline \text{Bin Range} & \text{Frequency} \\ \hline [29.5, 34.5] & 3 \\ [34.5, 39.5] & 17 \\ [39.5, 44.5] & 28 \\ [44.5, 49.5] & 47 \\ [49.5, 54.5] & 54 \\ [54.5, 59.5] & 31 \\ [59.5, 64.5] & 14 \\ [64.5, 69.5] & 4 \\ \hline \end{array}

STEP 6

To draw the histogram, you can use a graphical tool or software like Excel, Python (matplotlib), or any other tool capable of plotting histograms. The x-axis will represent the bin ranges, and the y-axis will represent the frequencies.
\begin{tikzpicture} \begin{axis}[ ybar, symbolic x coords={29.5-34.5, 34.5-39.5, 39.5-44.5, 44.5-49.5, 49.5-54.5, 54.5-59.5, 59.5-64.5, 64.5-69.5}, xtick=data, ylabel={Frequency}, xlabel={Bin Range}, nodes near coords, ymin=0, ] \addplot coordinates {(29.5-34.5, 3) (34.5-39.5, 17) (39.5-44.5, 28) (44.5-49.5, 47) (49.5-54.5, 54) (54.5-59.5, 31) (59.5-64.5, 14) (64.5-69.5, 4)}; \end{axis} \end{tikzpicture}

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