High School

Work out the mean of each set of numbers:

1. 8, 15, 18, 12, 13
2. 59, 78, 62, 67, 71, 73, 73, 72, 76, 70
3. 4.6, 5.3, 6.8, 2, 3.1, 2.1, 2.3, 1.3, 2.3, 1.2

Jeremy caught 8 fish in a contest. The mean weight of the fish was 4.2875 kg. He forgot to make his own record of the weight of the last fish, but the first 7 were: 4.4 kg, 5.1 kg, 6.6 kg, 2.7 kg, 3.6 kg, 4.9 kg, and 4 kg. What was the weight of the last fish?

Answer :

To find the mean of a set of numbers, you sum all the numbers in the set and then divide by the number of numbers in that set. Let's look at each question step-by-step:

  1. Set of Numbers: 8, 15, 18, 12, 13

    • First, add all the numbers together:
      [tex]8 + 15 + 18 + 12 + 13 = 66[/tex].
    • There are 5 numbers in this set.
    • Divide the sum by the number of numbers:
      [tex]\frac{66}{5} = 13.2[/tex].
    • So, the mean of the first set of numbers is [tex]13.2[/tex].

  2. Set of Numbers: 59, 78, 62, 67, 71, 73, 73, 72, 76, 70

    • Add all the numbers together:
      [tex]59 + 78 + 62 + 67 + 71 + 73 + 73 + 72 + 76 + 70 = 701[/tex].
    • There are 10 numbers in this set.
    • Divide the sum by the number of numbers:
      [tex]\frac{701}{10} = 70.1[/tex].
    • So, the mean of the second set of numbers is [tex]70.1[/tex].

  3. Set of Numbers: 4.6, 5.3, 6.8, 2, 3.1, 2.1, 2.3, 1.3, 2.3, 1.2

    • Add all the numbers together:
      [tex]4.6 + 5.3 + 6.8 + 2 + 3.1 + 2.1 + 2.3 + 1.3 + 2.3 + 1.2 = 31[/tex].
    • There are 10 numbers in this set.
    • Divide the sum by the number of numbers:
      [tex]\frac{31}{10} = 3.1[/tex].
    • So, the mean of the third set of numbers is [tex]3.1[/tex].

  4. Weight of the Last Fish

    • Jeremy caught 8 fish, with a mean weight of [tex]4.2875[/tex] kg.
    • The total weight of all 8 fish is:
      [tex]8 \times 4.2875 = 34.3[/tex] kg.
    • The weights of the first 7 fish are: [tex]4.4, 5.1, 6.6, 2.7, 3.6, 4.9,[/tex] and [tex]4[/tex].
    • Add the weights of the first 7 fish:
      [tex]4.4 + 5.1 + 6.6 + 2.7 + 3.6 + 4.9 + 4 = 31.3[/tex] kg.
    • To find the weight of the last fish, subtract the total weight of the first 7 fish from the total weight of all 8 fish:
      [tex]34.3 - 31.3 = 3[/tex] kg.
    • So, the weight of the last fish was [tex]3[/tex] kg.

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