document.write( "Question 1175748: Use the appropriate formula to find the mean,The madian,and the mode of each grouped data.
\n" ); document.write( "scores: Frequency:
\n" ); document.write( "46-50. 2
\n" ); document.write( "41-45. 9
\n" ); document.write( "36-40. 10
\n" ); document.write( "31-35. 14
\n" ); document.write( "26-30. 10
\n" ); document.write( "21-25. 5
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #850607 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Absolutely! Let's break down how to find the mean, median, and mode for this grouped data.\r
\n" ); document.write( "\n" ); document.write( "**1. Finding the Mean**\r
\n" ); document.write( "\n" ); document.write( "* **Midpoints:** First, find the midpoint of each class interval.
\n" ); document.write( " * 46-50: (46 + 50) / 2 = 48
\n" ); document.write( " * 41-45: (41 + 45) / 2 = 43
\n" ); document.write( " * 36-40: (36 + 40) / 2 = 38
\n" ); document.write( " * 31-35: (31 + 35) / 2 = 33
\n" ); document.write( " * 26-30: (26 + 30) / 2 = 28
\n" ); document.write( " * 21-25: (21 + 25) / 2 = 23\r
\n" ); document.write( "\n" ); document.write( "* **Multiply Midpoints by Frequencies:** Multiply each midpoint by its corresponding frequency.
\n" ); document.write( " * 48 * 2 = 96
\n" ); document.write( " * 43 * 9 = 387
\n" ); document.write( " * 38 * 10 = 380
\n" ); document.write( " * 33 * 12 = 396
\n" ); document.write( " * 28 * 7 = 196
\n" ); document.write( " * 23 * 5 = 115\r
\n" ); document.write( "\n" ); document.write( "* **Sum of (Midpoint * Frequency):** Add up the results from the previous step.
\n" ); document.write( " * 96 + 387 + 380 + 396 + 196 + 115 = 1570\r
\n" ); document.write( "\n" ); document.write( "* **Sum of Frequencies:** Add up all the frequencies.
\n" ); document.write( " * 2 + 9 + 10 + 12 + 7 + 5 = 45\r
\n" ); document.write( "\n" ); document.write( "* **Calculate the Mean:** Divide the sum of (midpoint * frequency) by the sum of frequencies.
\n" ); document.write( " * Mean = 1570 / 45 ≈ 34.89\r
\n" ); document.write( "\n" ); document.write( "**2. Finding the Median**\r
\n" ); document.write( "\n" ); document.write( "* **Cumulative Frequency:** Calculate the cumulative frequency.
\n" ); document.write( " * 2
\n" ); document.write( " * 2 + 9 = 11
\n" ); document.write( " * 11 + 10 = 21
\n" ); document.write( " * 21 + 12 = 33
\n" ); document.write( " * 33 + 7 = 40
\n" ); document.write( " * 40 + 5 = 45\r
\n" ); document.write( "\n" ); document.write( "* **Median Position:** Find the median position.
\n" ); document.write( " * Median position = (Total frequency + 1) / 2 = (45 + 1) / 2 = 23\r
\n" ); document.write( "\n" ); document.write( "* **Median Class:** Identify the class interval containing the median position. The 23rd value falls within the 36-40 class (cumulative frequency 21 to 33)\r
\n" ); document.write( "\n" ); document.write( "* **Median Formula (for grouped data):**
\n" ); document.write( " * Median = L + [(N/2 - CF) / f] * w
\n" ); document.write( " * Where:
\n" ); document.write( " * L = Lower boundary of the median class (35.5)
\n" ); document.write( " * N = Total frequency (45)
\n" ); document.write( " * CF = Cumulative frequency of the class before the median class (21)
\n" ); document.write( " * f = Frequency of the median class (12)
\n" ); document.write( " * w = Class width (5)
\n" ); document.write( " * Median = 35.5 + [(45/2 - 21) / 12] * 5
\n" ); document.write( " * Median = 35.5 + [(22.5 - 21) / 12] * 5
\n" ); document.write( " * Median = 35.5 + (1.5 / 12) * 5
\n" ); document.write( " * Median = 35.5 + (0.125) * 5
\n" ); document.write( " * Median = 35.5 + 0.625
\n" ); document.write( " * Median = 36.125\r
\n" ); document.write( "\n" ); document.write( "**3. Finding the Mode**\r
\n" ); document.write( "\n" ); document.write( "* **Modal Class:** Identify the class interval with the highest frequency. In this case, the 31-35 class has the highest frequency (12).\r
\n" ); document.write( "\n" ); document.write( "* **Mode Formula (for grouped data):**
\n" ); document.write( " * Mode = L + [(d1) / (d1 + d2)] * w
\n" ); document.write( " * Where:
\n" ); document.write( " * L = Lower boundary of the modal class (30.5)
\n" ); document.write( " * d1 = Frequency of the modal class - Frequency of the class before the modal class (12 - 10 = 2)
\n" ); document.write( " * d2 = Frequency of the modal class - Frequency of the class after the modal class (12 - 7 = 5)
\n" ); document.write( " * w = Class width (5)
\n" ); document.write( " * Mode = 30.5 + [2 / (2 + 5)] * 5
\n" ); document.write( " * Mode = 30.5 + (2 / 7) * 5
\n" ); document.write( " * Mode = 30.5 + (0.2857) * 5
\n" ); document.write( " * Mode = 30.5 + 1.4285
\n" ); document.write( " * Mode = 31.9285\r
\n" ); document.write( "\n" ); document.write( "**Summary**\r
\n" ); document.write( "\n" ); document.write( "* Mean: ≈ 34.89
\n" ); document.write( "* Median: ≈ 36.125
\n" ); document.write( "* Mode: ≈ 31.9285
\n" ); document.write( " \n" ); document.write( "
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