Calculate for me the mean ,median and mode

To calculate the mean, median, and mode for grouped data, we first need to set up a table with class midpoints and cumulative frequencies. Here's the data from the image: | Class Interval | Frequency (f_i) | |:--------------:|:-----------------:| | 1-5 | 12 | | 6-10 | 30 | | 11-15 | 9 | | 16-20 | 7 | | 21-25 | 6 | | 26-30 | 4 | Step 1: Prepare the table with midpoints and cumulative frequencies. We need the midpoint (x_i) for each class and the cumulative frequency (CF). The total frequency N = f_i = 12+30+9+7+6+4 = 68. | Class Interval | Frequency (f_i) | Midpoint (x_i) | f_i x_i | Cumulative Frequency (CF) | |:--------------:|:-----------------:|:----------------:|:---------:|:---------------------------:| | 1-5 | 12 | 3 | 36 | 12 | | 6-10 | 30 | 8 | 240 | 42 | | 11-15 | 9 | 13 | 117 | 51 | | 16-20 | 7 | 18 | 126 | 58 | | 21-25 | 6 | 23 | 138 | 64 | | 26-30 | 4 | 28 | 112 | 68 | | Total | N=68 | | 769 | | Step 2: Calculate the Mean. The formula for the mean of grouped data is: x = ( f_i x_i)/(N) Substitute the values from the table: x = (769)/(68) x ≈ 11.3088 Rounding to two decimal places, the mean is 11.31. Step 3: Calculate the Median. The formula for the median of grouped data is: Median = L + ( (N)/(2) - CFf ) × w First, find the median class. N/2 = 68/2 = 34. The 34th value falls in the class 6-10 (since its cumulative frequency is 42, which is the first CF greater than or equal to 34). • L (lower boundary of median class) = 6 - 0.5 = 5.5 • CF (cumulative frequency of class before median class) = 12 (for class 1-5) • f (frequency of median class) = 30 • w (class width) = 10.5 - 5.5 = 5 Substitute these values into the formula: Median = 5.5 + ( (34 - 12)/(30) ) × 5 Median = 5.5 + ( (22)/(30) ) × 5 Median = 5.5 + (110)/(30) Median = 5.5 + 3.666... Rounding to two decimal places, the median is 9.17. Step 4: Calculate the Mode. The formula for the mode of grouped data is: Mode = L + ( (f_m - f_1)/((f_m - f_1) + (f_m - f_2)) ) × w First, identify the modal class (the class with the highest frequency). The highest frequency is 30, which corresponds to the class 6-10. • L (lower boundary of modal class) = 6 - 0.5 = 5.5 • f_m (frequency of modal class) = 30 • f_1 (frequency of class before modal class) = 12 (for class 1-5) • f_2 (frequency of class after modal class) = 9 (for class 11-15) • w (class width) = 10.5 - 5.5 = 5 Substitute these values into the formula: Mode = 5.5 + ( (30 - 12)/((30 - 12) + (30 - 9)) ) × 5 Mode = 5.5 + ( (18)/(18 + 21) ) × 5 Mode = 5.5 + ( (18)/(39) ) × 5 Mode = 5.5 + (90)/(39) Mode = 5.5 + 2.307... Rounding to two decimal places, the mode is 7.81. Send me the next one 📸