Questions: RESULTS FROM SURVEY OF 110 FAMILIES Number of Children in the Family Number of Families 0 24 1 30 2 22 3 18 4 16 The table above shows the number of children in each of 110 families. What is the median number of children in these families? Find the least common multiple of 100 and 250.

RESULTS FROM SURVEY OF 110 FAMILIES

Number of Children in the Family  Number of Families
0  24
1  30
2  22
3  18
4  16

The table above shows the number of children in each of 110 families. What is the median number of children in these families?

Find the least common multiple of 100 and 250.
Transcript text: 35. RESULTS FROM SURVEY OF 110 FAMILIES \begin{tabular}{|c|c|} \begin{tabular}{c} Number of \\ Children in the \\ Family \end{tabular} & \begin{tabular}{c} Number of \\ Families \end{tabular} \\ \hline 0 & 24 \\ \hline 1 & 30 \\ \hline 2 & 22 \\ \hline 3 & 18 \\ \hline 4 & 16 \\ \hline \end{tabular} The table above shows the number of children in each of 110 families. What is the median number of children in these families? 36. Find the least common multiple of 100 and 250.
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Solution

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Solution Steps

Step 1: Calculate the cumulative number of families

We arrange the data in ascending order of the number of children. The cumulative number of families helps us find the median.

| Number of Children | Number of Families | Cumulative Number of Families | |---|---|---| | 0 | 24 | 24 | | 1 | 30 | 54 | | 2 | 22 | 76 | | 3 | 18 | 94 | | 4 | 16 | 110 |

Step 2: Find the position of the median

There are 110 families in total. Since this is an even number, the median will be the average of the values at positions 55 and 56.

Step 3: Determine the median

The cumulative number of families corresponding to 1 child is 54. This means the 54th family has 1 child. The 55th and 56th families have 2 children each. Thus, the median number of children is 2.

Final Answer

The median number of children is \(\boxed{2}\).

Step 1: Prime factorization of 100

\(100 = 2^2 \times 5^2\)

Step 2: Prime factorization of 250

\(250 = 2 \times 5^3\)

Step 3: Find the least common multiple (LCM)

The LCM is the product of the highest powers of all prime factors present in the numbers. In this case, the prime factors are 2 and 5. The highest power of 2 is \(2^2\). The highest power of 5 is \(5^3\).

Therefore, LCM(100, 250) = \(2^2 \times 5^3 = 4 \times 125 = 500\)

Final Answer

The least common multiple of 100 and 250 is \(\boxed{500}\).

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