15. Suppose data collected for heights (in cms) of 390 cows were tabulated in a frequency distribution and the following results were obtained. fi: \( 6,25,48,72,116,60,38,22,3 \) CMI \( =112, \mathrm{CM} 2=117 \) where CMi ith class mark Determine: a) Class interval size (class width), Class limits, Class boundaries and class marks b) The less than cumulative frequency distribution c) The class intervals having the highest frequency d) Above which height do we find \( 50 \% \) of the cows? c) Below which height do we get \( 25 \% \) of the cows? Draw a) histogram b) a frequency polygon c) C. a less than ogive for the above data

**Summary of Results:** - **Class Width**: 5 cm - **Class Limits**: - 110-115 cm - 115-120 cm - 120-125 cm - 125-130 cm - 130-135 cm - 135-140 cm - 140-145 cm - 145-150 cm - 150-155 cm - **Class Boundaries**: - 109.5-115.5 cm - 114.5-120.5 cm - 119.5-125.5 cm - 124.5-130.5 cm - 129.5-135.5 cm - 134.5-140.5 cm - 139.5-145.5 cm - 144.5-150.5 cm - 149.5-155.5 cm - **Class Marks**: - 112.5 cm - 117.5 cm - 122.5 cm - 127.5 cm - 132.5 cm - 137.5 cm - 142.5 cm - 147.5 cm - 152.5 cm - **Less Than Cumulative Frequency**: - 110-115: 6 - 115-120: 31 - 120-125: 79 - 125-130: 151 - 130-135: 267 - 135-140: 327 - 140-145: 365 - 145-150: 387 - 150-155: 390 - **Class with Highest Frequency**: 130-135 cm (116 cows) - **Height Above Which 50% of the Cows are Found**: 130-135 cm - **Height Below Which 25% of the Cows are Found**: 125-130 cm **Graphical Representations:** 1. **Histogram**: - X-axis: Height in cm - Y-axis: Frequency - Bars representing each class interval with heights corresponding to their frequencies. 2. **Frequency Polygon**: - Plots the class marks on the X-axis and frequencies on the Y-axis. - Connects the points with straight lines. 3. **Less Than Ogive**: - Plots the cumulative frequencies against the upper class boundaries. - Represents the cumulative distribution of the data. **Conclusion:** The frequency distribution provides a clear overview of the height distribution among the 390 cows, highlighting the most common height range and the distribution of cows above and below specific height thresholds. The graphical representations further aid in visualizing the data distribution effectively.