hmm, assuming that Fruit is in Column A for all Sheets
and, assuming that Number is in Column B for all Sheets,
then, for the Average Sheet:
<table style="width: 117pt; border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="156"><colgroup><col style="width: 69pt;" width="92"><col style="width: 48pt;" width="64"></colgroup><tbody><tr style="height: 15pt;" height="20"><td class="xl63" style="border: 0.5pt solid windowtext; width: 69pt; height: 15pt; background-color: transparent;" width="92" height="20">Apples</td><td class="xl63" style="border-width: 0.5pt 0.5pt 0.5pt medium; border-style: solid solid solid none; border-color: windowtext; width: 48pt; background-color: transparent;" align="right" width="64">10</td></tr><tr style="height: 15pt;" height="20"><td class="xl63" style="border-width: medium 0.5pt 0.5pt; border-style: none solid solid; border-color: windowtext; height: 15pt; background-color: transparent;" height="20">Pears</td><td class="xl63" style="border-width: medium 0.5pt 0.5pt medium; border-style: none solid solid none; border-color: windowtext; background-color: transparent;" align="right">15</td></tr><tr style="height: 15pt;" height="20"><td class="xl63" style="border-width: medium 0.5pt 0.5pt; border-style: none solid solid; border-color: windowtext; height: 15pt; background-color: transparent;" height="20">Appricots</td><td class="xl63" style="border-width: medium 0.5pt 0.5pt medium; border-style: none solid solid none; border-color: windowtext; background-color: transparent;" align="right">20</td></tr><tr style="height: 15pt;" height="20"><td class="xl63" style="border-width: medium 0.5pt 0.5pt; border-style: none solid solid; border-color: windowtext; height: 15pt; background-color: transparent;" height="20">Watermelons</td><td class="xl63" style="border-width: medium 0.5pt 0.5pt medium; border-style: none solid solid none; border-color: windowtext; background-color: transparent;" align="right">25</td></tr></tbody></table>
the formula in B1
=AVERAGE(SUMIF(INDIRECT("Sheet"&ROW(INDIRECT("1:10"))&"!A:A"),A1,INDIRECT("Sheet"&ROW(INDIRECT("1:10"))&"!B:B")))
Ctrl+Shift+Enter